Question

Let $f\left(x\right)=a{x}^{17}+b\sin x\sin 2x\sin 3x+c{x}^2\text{sgn}\left(\sin x\right)+d\log (x+\sqrt{1+x^2})+x(|x+1|-|x-1|)\left(\frac{e^x-e^{-x}}{e^x+e^{-x}}\right)$
be defined on the set of real numbers, (a > 0, b, c, d $\in$ R). If $f(-7)=7$, $f(-5)=-5$, $f(-2)=3$, then the minimum number of zeros of the equation $f\left(x\right)=0$ is

Answer 1

$f$ is an odd function $f\left(7\right)=-7,f\left(5\right)=5,f\left(2\right)=-3$
$x\to -\infty ,f\left(x\right)\to -\infty$
$x\to \infty ,f\left(x\right)\to \infty$
So, the minimum number of solution is $7.$